Unlike the NC, the QIM at large times is different from the static case derived in [1]}, [2]},
although curiously at the lowest order, \(g_{hh}dh^2\)  has the same form as the first correction to the
ground state complexity of Eq. (REF ), upon identifying \(dh \sim \delta \) . Importantly, here the \(t-t\) 
component of the metric on the branch coupled to the excited state of the central spin half system remains
the same as in the limit of small times, and hence at large times the QIM does not reduce to the static
situation.
